If a miner includes a proof from another miner, then the total power of the network increases, reducing this miners expected future reward. So at a glance, it seems irational for miners to include proof messages. How does this work?
So the strictly money based answer to this is that a miner with X% of the networks power will include a message adding a proof that would result in an expected reward of Y FIL, requires a transaction fee of at least X% of Y in order for it to be rational to include it.
This isnt terrible, one small example:
A miner with 500 sectors committed, in a network with 100,000 sectors, with a block reward of 10FIL/block (that number pulled out of my ass) (and also making the assumption that sectors last for about three months) will mine a message adding one more sector if it includes a fee of 0.126FIL. While the miner adding that proof stands to make 25.9FIL in that time period. That is, the fee is (500 / 100000) * 25.9.
Stopping here quickly to acknowledge some of the factors i'm not yet taking into account:
- continued growth in the network causing that expected reward number to be wrong (too high)
- an incentive of miners to include more proofs because it increases the weight of their chain
Continuing. With the (likely bad) assumption that most miners in the network have the same ratio of the network, then proof messages with that fee will be mined immediately. But whats interesting here is what happens when the distributions of miners are heterogenous. If the 500/100,000 miner (0.5%) is the largest miner (unlikely, but lets talk about it) then the fee that the proof submitter should add should be less than 0.126, because other smaller miners will accept a smaller fee. If the 0.5% miner is rational, they should see that that proof would be included anyways and mine it anyways, as otherwise they would be missing out on those transaction fees (note: assuming a non-full mempool, which given other calculations may be a horrible assumption). The effect here is that the more the network is comprised of small miners (ex: 50% of the total power is provided by miners with 0.1% or less of the power) the more likely proofs are to be included at reasonable rates and within reasonable time spans.
The next step here without taking the previously mentioned ignored factors, is to look at expected rewards based on average delays at different fee levels. A miner with 20% of the networks power is going to want a very large fee on their own, but if the network configuration contains a large percentage of miners who are willing to accept lower fees, then the question that miner needs to answer is: What is my expected profit difference between now and between the time in the future expected time that the message will be mined. The difference is the premium on top of a minimum fee that miner should charge to effectively break even.
So for each miner, the adjusted fee that they should accept looks like:
[ insert math ]